This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Final Fantasy Type-0
The introduction alone sets the tone for the rest of the game. You see teenagers gunned down by assault rifles, soldiers stopping to shoot at the wounded laying at their feet, and during the stage itself you run across a wounded Bahamut laying on its side roaring in pain with blood streaked across its scales.
Izana's death. He fails to keep up a brave face and spends his final moments crying as he wishes he could live. Not to mention his beloved chocobo dies with him. And that's just the intro!
Dear God, the ending scene where Class Zero chat about their future dreams and sing a song to comfort each other as they slowly and painfully succumb to their wounds. By the time Machina and Rem arrive, they're all lying dead in a huddle, holding hands.
And Ace sings "Zero", trying to comfort his partners. One would think the song sounds beautiful, but it only adds to the Tear Jerker once you know what he's singing, and the rest of the song.
Kurasame's death, and Caetuna being crystalized.
Worse, Cater and Nine, who both said they'd never forget what he was like and that he was taking the mission to help them, are the two most critical of what he was like based on his mission report. Nine had a brief moment when he felt like they shouldn't be acting that way, but it passed. Even Kazusa himself feels something is missing and looks for something to confirm he knew the man.
Emina being a spy was because she was rescued by the empire when the war took her home from her and then trained to be a spy after being branded. She turned herself in for being a spy due to Class Zero. She was executed and no one remembers her afterwards.
When Carla's Crimson Codex profile reveals that the money she's been asking from you is actually going towards her dying mother's medical bills, and supporting her little sister in taking care of her. Kinda makes you feel bad about being stingy with your gil, doesn't it?
Aria's death at the hands of Milites soldiers. Both the fakeout and the real one late in the game. The only reason she was still on the base to get shot is because she had become loyal to Qator and refused to leave back to the dominion when offered, leading to her being killed because of a Nice Guy who she couldn't remember.
Machina accidentally killing Rem, whose final request is that he remember her. Machina then sobs over her corpse before going into crystal stasis.
On the final level, all of Class Zero are so severely injured they're limping into battle. You feel nearly helpless as they struggle against the Rursan Arbiter until Rem and Machina empower them.
A second playthrough unlocks an Another Side, Another Story moment where you find out what Machina was doing during the final battle against Milites — you take control of him in Ingram, in l'Cie mode with no memories, slicing up Suzaku students as they Zerg Rush him to no avail, and he can absorb Phantoma from their corpses. Not only will you feel like a right heel, but then the Player Punch kicks in when you realize this is exactly what Class Zero has been doing to Milites the entire game.
When it is revealed that Rem is dying because of an incurable disease and is choosing to keep this from Machina and the rest of Class Zero.
Machina and Rem's past and why they came to Akademia in the first place. Their village was attacked by a malboro that infected almost everyone with an illness. Their village lay on the border between Rubrum and Milites regions and Milites decided to handle this by burning the village and everybody in it. Machina and Rem were only children, but they managed to run away. Though it seems that Rem was infected by the disease, which is incurable.
This is worse for Izana. He was outside of the village when all this was happening. Then he comes back to find his home burned down. This also drives a wedge between Izana and Machina for a while after.
It is revealed in one of Ace's dream sequences that Izana was actually jealous of Machina because the latter is an elite cadet while Izana is just a legionary. This leads to Ace requesting for Izana to join him on the mission that eventually gets him killed.